Today's tough is isomorphic to 09/20's.
Proof :
1) Turn today's grid 90° counterclockwise.
2) Exchange columns 1 and 2, exchange columns 9 and 8 .
3) Exchange columns 2 and 3, exchange columns 8 an 7.
4) Substitute numbers this way : 1->7->5->4->9->8->2->3->1.
What do you think you get now? Exactly 09/20's tough grid.
Now please note that operations 1,2,3,4 transform a correct solution of today's into a correct solution of 09/20's. Furthermore, operations 1,2,3,4 can be backed (beware the order) to transform a correct solution of 09/20's into a correct solution of today's.

Think a bit and you'll realize that there's no point in proving again uniqueness of today's, as it suffices to transform 09/20's proof (find it in "proofs" link) by operations 4backed, 3backed, 2backed, 1backed to obtain today's proof of uniqueness.

My apologies to mathematician readers, as all this is clearly evident to them and needs not developing.

My apologies also to non-mathematician readers, as all this must seem a little theoretic to them and needing more explanations.

Eventually, for what reader exactly did I post all this?